Numerical investigation of wall pressure fluctuations for zero and adverse pressure gradient turbulent boundary layers using synthetic anisotropic turbulence

Abstract

Pressure uctuations within turbulent boundary layers on a at plate conguration are simulated using synthetic isotropic and anisotropic turbulence generated by the Fast Random Particle-Mesh Method. The averaged turbulence statistics needed for the stochastic realization is provided by a Reynolds averaged Navier-Stokes calculation. Dierent integral length scales in dierent directions are used to realize the anisotropy of the turbulence length scales. Reynolds stress anisotropy is implemented by relating the anisotropic Reynolds stresses obtained from the Reynolds averaged Navier-Stokes calculation and the respective isotropic Reynolds stresses realized from the Fast Random Particle-Mesh Method. Wall pressure uctuations are obtained by solving a Poisson equation including both the mean-shear turbulence interaction source term and the turbulence-turbulence interaction source term. The Poisson equation is solved using the convolution theorem in wavenumber domain and with a free-space Green function. For an exact realization of the Green function in conjunction with a Fourier transform method on a nite domain, Hockney's method is applied to the Poisson problem. Wall pressure uctuations for zero and adverse pressure gradient boundary layers are calculated. The adverse pressure gradient is realized by placing an airfoil above the at plate. Simulated one-point spectra and two-point statistics are analyzed. Simulated results for the wall pressure one-point spectra show that spectra from both the mean-shear term and the turbulence-turbulence term have the same order of magnitude. The results are compared to the experimental results, which were acquired in the Acoustic Windtunnel Braunschweig for the same congurations.

CFD-based study on one- and two-point statistics of wall pressure fluctuations

“…Two-dimensional (2D) RANS calculations for the three cases were conducted using the differential Reynolds stress model with a g-equation 32 . 33 For details about the measurement and RANS calculation, the reader is referred to Hu and Herr 4 and Hu et al 33 The boundary layer parameters for the selected cases are summarized in Table 1, which were determined at x 1 = 1210 mm on the flat plate. The results from RANS are in good agreement with the measurement results, except for the boundary layer thickness for the APG case which is too thin compared to the measurement result.…”

On the Modeling of Wall Surface Pressure Spectra for Trailing Edge Noise Prediction

“…While numerical methods like stochastic, synthetic turbulence [6][7][8], large eddy simulation [9][10][11], or direct numerical simulation [12][13][14][15] techniques have also been applied to study trailing edge noise, these models are not attractive for the integration in fast design tools. However, the detailed insights into the flow structures can help to advance analytical methods.…”